A168644 - cp's OEIS frontend

A168644 Triangle read by rows: T(n, k) = [x^k] p(x,n), where p(x,0) = 1, p(x,n) = (7 - n)(1+x)^n - (6-n)(1 + x^n) for 1 <= n <= 5, and p(x,n) = 5(1 + x)^n - Sum_{i=0..3} (Sum_{j=0..i} binomial(n, j)(x^j + x^(n-j))) + (1/6)n(n - 1)(n - 5)x^(n-3) for n >= 6.

n	a(n)
0	1
1	1
2	1
3	1
4	10
5	1
6	1
7	12
8	12
9	1
10	1
11	12
12	18
13	12
14	1
15	1
16	10
17	20
18	20
19	10
20	1
21	1
22	12
23	45
24	65
25	45
26	12
27	1
28	1
29	14
30	63
31	140
32	154
33	63
34	14
35	1
36	1
37	16
38	84
39	224
40	350
41	252
42	84
43	16
44	1
45	1
46	18
47	108
48	336
49	630
50	630
51	384
52	108
53	18
54	1
55	1
56	20
57	135
58	480
59	1050
60	1260
61	1050
62	555
63	135
64	20
65	1

[1, 1, 1, 1, 10, 1, 1, 12, 12, 1, 1, 12, 18, 12, 1, 1, 10, 20, 20, 10, 1, 1, 12, 45, 65, 45, 12, 1, 1, 14, 63, 140, 154, 63, 14, 1, 1, 16, 84, 224, 350, 252, 84, 16, 1, 1, 18, 108, 336, 630, 630, 384, 108, 18, 1, 1, 20, 135, 480, 1050, 1260, 1050, 555, 135, 20, 1]

cp's OEIS Frontend

A168644 Triangle read by rows: T(n, k) = [x^k] p(x,n), where p(x,0) = 1, p(x,n) = (7 - n)(1+x)^n - (6-n)(1 + x^n) for 1 <= n <= 5, and p(x,n) = 5(1 + x)^n - Sum_{i=0..3} (Sum_{j=0..i} binomial(n, j)(x^j + x^(n-j))) + (1/6)n(n - 1)(n - 5)x^(n-3) for n >= 6.

Table of values

List of values

cp's OEIS Frontend

A168644 Triangle read by rows: T(n, k) = [x^k] p(x,n), where p(x,0) = 1, p(x,n) = (7 - n)*(1+x)^n - (6-n)*(1 + x^n) for 1 <= n <= 5, and p(x,n) = 5*(1 + x)^n - Sum_{i=0..3} (Sum_{j=0..i} binomial(n, j)*(x^j + x^(n-j))) + (1/6)*n*(n - 1)*(n - 5)*x^(n-3) for n >= 6.

Table of values

List of values

A168644 Triangle read by rows: T(n, k) = [x^k] p(x,n), where p(x,0) = 1, p(x,n) = (7 - n)(1+x)^n - (6-n)(1 + x^n) for 1 <= n <= 5, and p(x,n) = 5(1 + x)^n - Sum_{i=0..3} (Sum_{j=0..i} binomial(n, j)(x^j + x^(n-j))) + (1/6)n(n - 1)(n - 5)x^(n-3) for n >= 6.